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Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

In the field of reliability engineering, the Active learning reliability method combining Kriging and Monte Carlo Simulation (AK-MCS) has been developed and demonstrated to be effective in reliability analysis. However, the performance of…

The existing core methods, which are employed by the popular CTL model checking tools, are facing the famous state explode problem. In our previous study, a method based on the Machine Learning (ML) algorithms was proposed to address this…

Numerical N-body simulations are commonly used to explore stability regions around exoplanets, offering insights into the possible existence of satellites and ring systems. This study aims to utilize Machine Learning (ML) techniques to…

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…

We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…

The predictive capabilities of machine learning (ML) models used in materials discovery are typically measured using simple statistics such as the root-mean-square error (RMSE) or the coefficient of determination ($r^2$) between…

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

The increasing scale and complexity of global supply chains have led to new challenges spanning various fields, such as supply chain disruptions due to long waiting lines at the ports, material shortages, and inflation. Coupled with the…

Multi-fidelity Reinforcement Learning (RL) frameworks efficiently utilize computational resources by integrating analysis models of varying accuracy and costs. The prevailing methodologies, characterized by transfer learning, human-inspired…

Inverse uncertainty quantification (UQ) tasks such as parameter estimation are computationally demanding whenever dealing with physics-based models, and typically require repeated evaluations of complex numerical solvers. When partial…

We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to…

Many practical problems involve estimating low dimensional statistical quantities with high-dimensional models and datasets. Several approaches address these estimation tasks based on the theory of influence functions, such as…

Computationally efficient and accurate simulations of the flow over axisymmetric bodies of revolution (ABR) has been an important desideratum for engineering design. In this article the flow field over an ABR is predicted using machine…

Distributionally Robust Reinforcement Learning (DR-RL) aims to derive a policy optimizing the worst-case performance within a predefined uncertainty set. Despite extensive research, previous DR-RL algorithms have predominantly favored…

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…

While machine learning (ML) post-processing of convection-allowing model (CAM) output for severe weather hazards (large hail, damaging winds, and/or tornadoes) has shown promise for very short lead times (0-3 hours), its application to…

Amyotrophic Lateral Sclerosis (ALS) is characterized as a rapidly progressive neurodegenerative disease that presents individuals with limited treatment options in the realm of medical interventions and therapies. The disease showcases a…

In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…